Based on the results of Prob. 4–86E, verify that this converging duct flow field is indeed incompressible.

Converging duct flow is modeled by the steady, two-dimensional velocity field. For the case in which U₀ = 5.0 ft/s and b = 4.6 s^–1, consider an initially square fluid particle of edge dimension 0.5 ft, centered at x = 0.5 ft and y = 1.0 ft at t = 0 (Fig. P4–86E). Carefully calculate and plot where the fluid particle will be and what it will look like at time t = 0.2 s later. Comment on the fluid particle’s distortion.

FIGURE P4–86

Transcribed Image Text:

X Initially square fluid particle at t = 0 Unknown shape and location of fluid particle at later time t